EDEXCEL GCSE FOUNDATION MATHS - What are Enlargements

Edexcel GCSE Foundation Maths: What are Enlargements?

Understanding Enlargements

An enlargement is a transformation that changes the size of a shape. It does this by multiplying all the lengths of the shape by the same number, called the scale factor.

Key Terms

• Scale Factor: The number that all the lengths of a shape are multiplied by in an enlargement.
• Centre of Enlargement: The fixed point from which all the lengths are measured.
• Image: The new shape after the enlargement.
• Object: The original shape before the enlargement.

Types of Enlargements

• Positive Scale Factor: The image is larger than the object.
• Negative Scale Factor: The image is smaller than the object and reflected.
• Scale Factor of 1: The image is the same size as the object.

Steps to Perform an Enlargement

1. Identify the Centre of Enlargement: This is the fixed point from which all measurements are taken.
2. Draw Lines from the Centre of Enlargement to Each Corner of the Object: These lines are called rays.
3. Multiply the Distance from the Centre of Enlargement to Each Corner by the Scale Factor: This gives you the new distances for the image.
4. Mark the New Points on the Rays: These points form the corners of the image.
5. Join the New Points: This creates the image of the enlarged shape.

Example

Enlarge triangle ABC with a scale factor of 2 and centre of enlargement O:

[Insert diagram here]

Steps

1. Identify the centre of enlargement (O).
2. Draw lines from O to each corner of triangle ABC.
3. Multiply the distance from O to A, O to B, and O to C by 2. This gives you the new distances for the image.
4. Mark the new points on the rays (A', B', and C').
5. Join A', B', and C' to form the image of triangle ABC.

Important Note: The image of an enlargement is similar to the object. This means the shapes are the same but different sizes.

Practice Questions

1. Enlarge the rectangle below with a scale factor of 3 and centre of enlargement O:

   [Insert rectangle diagram here]

2. Enlarge the triangle below with a scale factor of -2 and centre of enlargement O:

   [Insert triangle diagram here]

Remember: Enlargements are a fundamental transformation in geometry and understanding them will help you tackle more complex problems in Edexcel GCSE Foundation Maths.